Chapter 3Hydraulic circuit analysis

The previous chapters have introduced the governing equations for fluid flow and provided solutions for simple
unidirectional flows. While we can only rarely use these simple solutions to exactly describe real flows, these
unidirectional flows provide a framework for generating engineering estimates for many flows, and these estimation
techniques reduce complex systems with large numbers of components into a relatively simple approximate linear
description. This is relevant for flow in microdevices both (1) because microdevices can straightforwardly be made
with large numbers of microchannels and (2) because those microchannels often have a geometry that
leads to flows that are well approximated by the unidirectional solutions presented in Chapter 2. Our
approach, called hydraulic circuit analysis, involves assuming that the Poiseuille flow derived in Chapter 2
provides a sound engineering estimate of the pressure drops and flow rates through long, mostly straight
channels, even if the cross section is not exactly circular and the channels are neither perfectly straight
nor infinite in extent. We thus write an approximate linear relation between pressure drops and flow
rates through these channels—the Hagen-Poiseuille law. This law, combined with conservation of
mass, approximately prescribes fluid flow through complex networks by solution of sets of algebraic
equations.